Exponents

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lj: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jan 04, 2011 9:05 pm

by lj » Sat Feb 12, 2011 5:18 pm

Could someone please advise on how the solve the problem below ? Thanks

Q: what is the units digit of (13)^4 (17)^2 (29)^3

a. 9
b. 7
c. 5
d. 3
e. 1

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Source: Beat The GMAT — Problem Solving | Sat Feb 12, 2011 5:18 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 12, 2011 6:48 pm

lj wrote:Could someone please advise on how the solve the problem below ? Thanks

Q: what is the units digit of (13)^4 (17)^2 (29)^3

a. 9
b. 7
c. 5
d. 3
e. 1

(1)*(9)*(9)=(1)
IOM E

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lj: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jan 04, 2011 9:05 pm

by lj » Sun Feb 13, 2011 4:58 pm

Night reader wrote:
lj wrote:Could someone please advise on how the solve the problem below ? Thanks

Q: what is the units digit of (13)^4 (17)^2 (29)^3

a. 9
b. 7
c. 5
d. 3
e. 1
(1)*(9)*(9)=(1)
IOM E

Thanks for the help. How did you get those numbers ? Cant seem to figure that part out .

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Ashish8: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Jan 23, 2010 9:08 pm; Thanked: 2 times

by Ashish8 » Sun Feb 13, 2011 5:43 pm

I also agree with Night Reader E

3 * 3 * 3 * 3 = units digit of 1

7 * 7 = units digit of 9

9 * 9 * 9 = units digits of 9

We just need to multiply the units digits cause anything else doesn't affect the product of the units digit.

9 * 9 * 1 = units digit of 1.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 14, 2011 5:44 am

lj wrote:What is the units digit of (13)^4 (17)^2 (29)^3 ?

a. 9
b. 7
c. 5
d. 3
e. 1

Unit's digit of (13^4)*(17^2)*(29^3) will be same as the unit's digit of the product of unit's digits of (13^4), (17^2), and (29^3).

Now, unit's digit of

(13^4) = unit's digit of (3^4) = 1
(17^2) = unit's digit of (7^2) = 9
(29^3) = unit's digit of (9^3) = 9

Hence, required unit's digit = unit's digit of the product of 1, 9, and 9 = unit's digit of 81 = 1

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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